Information processing apparatus and computer-readable recording medium storing battery deterioration diagnosis program

ABSTRACT

An information processing apparatus includes: a memory; and a processor coupled to the memory and configured to: obtain an actual measurement voltage at a time of a voltage change of a battery; estimate an internal impedance of the battery based on an equivalent circuit model of the battery in which a Warburg impedance is represented by an approximate equation using an equivalent circuit which is a series circuit of CR circuits and has steps of a power of 10 as a time constant of the CR circuit and the actual measurement voltage; determine a deterioration state of the battery based on the internal impedance; and notify of deterioration of the battery in a case where the deterioration diagnosis unit detects deterioration.

CROSS-REFERENCE TO RELATED APPLICATION

This application is based upon and claims the benefit of priority of theprior Japanese Patent Application No. 2019-18229, filed on Feb. 4, 2019,the entire contents of which are incorporated herein by reference.

FIELD

The embodiment discussed herein is related to a battery deteriorationdiagnosis apparatus, a battery deterioration analysis circuit, and acomputer-readable recording medium storing a battery deteriorationdiagnosis program,

BACKGROUND

In order to realize a low carbon society or efficiently use energy, anincrease in utilization of energy devices such as photovoltaic powergeneration (PV), storage batteries is expected. When a large amount ofenergy supply devices such as photovoltaic power generation areintroduced into a power system, there is a concern that a largeinfluence is exerted on reception operation of a power company due tothe output fluctuation. In order to perform a stable system operation,it is desired to consider countermeasures such as reducing a rate ofchange in demand by using equipment such as a heat pump type waterheater, a storage battery.

Examples of the related art include Japanese Laid-open PatentPublication No. 2011-141228, Japanese Laid-open Patent. Publication No.2015-206758, Japanese Laid-open Patent Publication No. 2005-274280, andJapanese. Laid-open Patent. Publication No. 2017-16991.

SUMMARY

According to an aspect of the embodiments, an information processingapparatus includes: a memory; and a processor coupled to the memory andconfigured to: obtain an actual measurement voltage at a time of avoltage change of a battery; estimate an internal impedance of thebattery based on an equivalent circuit model of the battery in which aWarburg impedance is represented by an approximate equation using anequivalent circuit which is a series circuit of CR circuits and hassteps of a power of 10 as a time constant of the CR circuit and theactual measurement voltage; determine a deterioration state of thebattery based on the internal impedance; and notify of deterioration ofthe battery in a case where the deterioration diagnosis unit detectsdeterioration.

The object and advantages of the invention will be realized and attainedby means of the elements and combinations particularly pointed out inthe claims.

It is to be understood that both the foregoing general description andthe following detailed description are exemplary and explanatory and arenot restrictive of the invention.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram illustrating a battery deterioration diagnosissystem according to an embodiment;

FIG. 2 is a diagram illustrating an equivalent circuit model of abattery;

FIG. 3 is a diagram illustrating an equivalent circuit of a Warburgimpedance;

FIG. 4 is a diagram illustrating an example of a parameter value in acase where the Warburg impedance is represented by the equivalentcircuit;

FIG. 5 is a diagram for explaining an overlap of first order LPFcharacteristics;

FIG. 6 is a diagram illustrating a comparison between an estimatedwaveform using an approximate solution and a waveform based on an actualmeasurement value;

FIG. 7 is a block diagram of a deterioration diagnosis server;

FIG. 8 is a flowchart of an estimation process of an equivalent circuitparameter;

FIG. 9 is a flowchart of a deterioration diagnosis process;

FIG. 10 is a diagram illustrating an example of an analysis result of aninternal impedance;

FIG. 11 is a diagram illustrating an estimated value of an equivalentcircuit parameter in a case where a battery of 4.5 Ah is used;

FIG. 12 is a diagram illustrating an actual measurement value in a casewhere a battery of 4.5 Ah is used;

FIG. 13 is a diagram illustrating an estimated value of an equivalentcircuit parameter in a case where a battery of 8.0 Ah is used;

FIG. 14 is a diagram illustrating an actual measurement value in a casewhere the battery of 8.0 Ah is used; and

FIG. 15 is a hardware configuration diagram of the deteriorationdiagnosis server.

DESCRIPTION OF EMBODIMENTS

As one method of adjusting the demand using such various devices, a useof a demand response (DR) may be considered. The demand response is atechnology of adjusting a demand by providing an economic merit. Forexample, as utilization of the demand response, there is a demandadjustment for controlling a storage battery of a consumer by giving anincentive or a penalty to charge and discharge of the storage battery ofthe consumer. In order to more efficiently utilize the demand response,it is desirable to use solar power generation, wind power generation, anenergy management system using a co-generator and a storage battery.

In order to significantly deal with the demand response, it is importantto accurately grasp a state of a storage battery system. In order toaccurately grasp the state of the storage battery system, an appropriatedeterioration diagnosis of the storage battery system is required. Onemethod of diagnosing deterioration in the storage battery system is, forexample, a method in which charge and discharge are actually performedto measure a discharge capacity. Meanwhile, in the method of actuallyperforming charge and discharge, measurement for a long time isperformed, and rapid diagnosis is difficult, and this also may be afactor or deteriorating the storage battery.

Another method of diagnosing deterioration in the storage battery systemis to evaluate deterioration of the storage battery system by using achange in a direct current (DC) resistance. Meanwhile, since the DCresistance is a resistance of approximate milliohm, a measurement erroris large, so a deterioration diagnosis performance is poor and it isdifficult to use the DC resistance in an actual operation.

There is also a deterioration diagnosis using an internal equivalentmodel of a storage battery. For example, in the internal equivalentcircuit model of the storage battery, a parallel circuit of a resistorand a capacitor is disposed together with a DC resistor. In a case wherethe storage battery is deteriorated, a change in a resistance in theparallel circuit is larger than a change in a resistance of the DCresistor. Therefore, by detecting the change in the resistance in theparallel circuit in the internal equivalent circuit model of the storagebattery, it is possible to perform deterioration diagnosis with highaccuracy.

In order to measure a resistance value of the resistor in the parallelcircuit in the internal equivalent circuit model of the storage battery,an AC method using a frequency domain or an analysis using a transientresponse using a time domain is used. In an accurate deteriorationdiagnosis for the storage battery system, impedance measurement using acurrent at the time of an actual operation is required.

In the measurement of internal impedance by the AC method, a method ofmeasuring the internal impedance from a frequency change of a minutealternating current (AC) signal is used. Meanwhile, since a DCresistance in the internal equivalent circuit model of the storagebattery or a resistance in the parallel circuit has a currentdependency, it is difficult to obtain the resistance value in the actualoperation. Therefore, in a case of more accurately performingdeterioration diagnosis on the storage battery system, it is appropriateto use analysis by a transient response characteristic.

The internal impedance of the storage battery includes a Warburgimpedance component of ion conduction. Although the Warburg impedancecomponent may be easily calculated when a current change is an idealstep change such as a Heaviside step function, it is difficult tocalculate the impedance component since waveform distortion is usuallygenerated. In the storage battery system, since an ion conductivecomponent is coupled to a capacitance, it takes a long time to calculatethe impedance. In a case of calculating the impedance, since thecalculation requires much time and power when solving a combinationaloptimization problem, it is required to perform the analysis with asmall amount of calculation.

Therefore, an approximation method using an equivalent model using afoster type circuit is considered to be used to obtain the impedancecomponent of the Warburg impedance component. In a case of theapproximation method using the equivalent model using the foster typecircuit, a frequency range used for diffraction is as follows, Foranalyzing a capacitor resistance (CR) time constant of several 10 ofmsec, 1 kHz is used as a sampling frequency. According to a samplingtheorem, a frequency of 1 kHz does not include information equal to ormore than 500 Hz. It takes 1 second to analyze the internal impedance ofthe storage battery. In a frequency range of the analysis for 1 second,the analysis is performed up to a frequency of 0.5 Hz. For example,since analysis for a frequency of 500 Hz is performed each 0.5 Hz, in acase of the approximation method using the equivalent model using thefoster type circuit, a frequency response range of at least 3 digits isanalyzed.

As a technology of evaluating a battery characteristic in considerationof a Warburg impedance, a current waveform is divided into minute stepfunctions, and transient response waveforms are calculated by synthesisof the step functions. For example, an AC signal is applied to asecondary battery to estimate a Warburg impedance, and a circuitparameter is estimated from a transient response waveform of a currentvoltage. As another technology of diagnosing deterioration, a deviationbetween a terminal voltage measured for each minute unit correspondingto a discharge current and a calculated voltage is calsulated, and aconstant of an element of an equivalent circuit is obtained so that adeviation square sum or a deviation average becomes small so as todetermine a state of the battery. For example, data at a transientresponse is extracted from current measurement data of a secondarybattery, and a circuit parameter of an electric equivalent circuit atcompletion of discharge of the secondary battery is obtained, anddeterioration diagnosis is performed.

Meanwhile, in an equivalent model using a normal foster type circuit, atime constant of each CR circuit is set to (2n−1)². Therefore, in orderto obtain a frequency response range of 3 digits, 16 CR circuits areused, and it is difficult to suppress the amount of calculation.

When a transient response waveform is calculated by a step functionsynthesis method, since elements from the beginning are stacked, highlyaccurate calculation easily affected by an error is required. It isrequired to perform the calculation until completion of analysis on alldivided steps, and in a case where the number of divisions is increasedto improve calculation accuracy, the amount of calculation is increased.Since a calculation time or an error varies depending on the number ofdivisions, the number of divisions is optimized for each waveform to beanalyzed, so the amount of calculation is increased.

It is difficult to apply the technology in which an AC signal is appliedto a secondary battery to estimate a Warburg impedance, to a storagebattery which outputs DC electricity. A constant of an element of anequivalent circuit is obtained from deviation between a terminal voltageand a calculated voltage for each minute unit or data at the time of atransient response is extracted from measurement data to obtain acircuit parameter, a Warburg impedance is not considered, and it isdifficult to perform deterioration diagnosis with accuracy.

A battery deterioration diagnosis apparatus, a battery deteriorationanalysis circuit, and a computer-readable recording medium storing abattery deterioration diagnosis program capable of accurately performinglife diagnosis on a storage battery with a small amount of calculationmay be provided.

Hereinafter, an embodiment of a battery deterioration diagnosisapparatus, a battery deterioration analysis circuit, and acomputer-readable recording medium storing a battery deteriorationdiagnosis program disclosed in the present application will be describedin detail with reference to the drawings. The battery deteriorationdiagnosis apparatus, the battery deterioration analysis circuit, and thecomputer-readable recording medium storing the battery deteriorationdiagnosis program disclosed in the present application are not limitedto the embodiment to be described below.

EMBODIMENT

FIG. 1 is a diagram illustrating a battery deterioration diagnosissystem according to the embodiment. An electronic deteriorationdiagnosis system 7 includes a deterioration diagnosis server 1, a datacollection system 2, a battery 3, a load 4, a voltage sensor 5, and acurrent sensor 6.

One or a plurality of batteries 3 are coupled in series. The battery 3is, for example, a lead-acid battery. The battery 3 is mounted on, forexample, an uninterruptible power supply (UPS).

The load 4 is coupled to the battery 3. The load 4 is driven byreceiving power supplied from the battery 3. The load 4 is, for example,an information processing device.

The voltage sensor 5 is disposed in the same number as the battery 3,and is coupled in parallel with the battery 3. When each voltage sensor5 receives a load change signal indicating occurrence of a load changein the load 4, the voltage sensor 5 starts measurement of a voltagevalue of the corresponding battery 3, and transmits the measurementresult to the data collection system 2. The load change signal is asignal input from a manager to the voltage sensor 5 and the currentsensor 6.

The current sensor 6 is coupled in series with the battery 3. When aload change signal is received, the current sensor 6 measures a currentvalue flowing through a load 4 supplied from one or a series ofbatteries 3 coupled in series.

The data collection system 2 is, for example, a communication devicesuch as a router. The data collection system 2 collects voltagemeasurement data which is a voltage value of each battery 3 measured byeach voltage sensor 5, and current measurement data which is a currentvalue flowing through the load 4 measured by the current sensor 6. Thedata collection system 2 outputs the collected voltage measurement dataand current measurement data to the deterioration diagnosis server 1.

The deterioration diagnosis server 1 is a device for diagnosingdeterioration of the battery 3. The deterioration diagnosis server 1receives an input of the voltage measurement data and currentmeasurement data from the data collection system 2. The deteriorationdiagnosis server 1 determines a deterioration state of the battery 3 byusing the voltage measurement data and the current measurement data. Ina case where the deterioration of the battery 3 is detected, thedeterioration diagnosis server 1 notifies the manager of thedeterioration of the battery 3 by displaying a warning message or thelike.

Hereinafter, determination of the deterioration state by thedeterioration diagnosis server 1 will be described below. Thedeterioration diagnosis server 1 has a parameter value in advanceincluded in an equivalent circuit model to be described below in a casewhere the battery 3 is represented by using the equivalent circuitmodel. Hereinafter, the parameter included in the equivalent circuitmodel representing the battery 3 is referred to as an “equivalentcircuit parameter”.

FIG. 2 is a diagram illustrating an equivalent circuit model of abattery. In the present embodiment, the equivalent circuit model 10illustrated in FIG. 2 is used as an equivalent circuit model of thebattery 3. The equivalent circuit model 10 is an equivalent circuit inwhich the Warburg impedance is coupled to a CR circuit in series, and isa model in which the CR circuit is added to an equivalent circuit modelcalled a Modified Randles model.

In the equivalent circuit model 10, a DC power supply 11 and a resistor12 are coupled in series. A CR circuit in which a resistor 13 and acapacitor 14 are coupled in parallel, and a CR circuit in which aresistor 15 and a capacitor 16 are coupled in parallel are coupled tothe resistor 12 in series. A Warburg impedance 17 is coupled in seriesto the CR circuit including the resistor 15 and the capacitor 16.

An output voltage of the DC power supply 11 is an open circuit voltage(OCV). A resistance value of the resistor 12 is R0. A resistance valueof the resistor 13 is R. A capacitance of the capacitor 14 is C1. Aresistance value of the resistor 15 is R2. A capacitance of thecapacitor 16 is C2. An impedance of the Warburg impedance 17 is Zw. R0to R3, C1 and C2, and Dw are equivalent circuit parameters.

At this time, in a case where the battery 3 is represented by theequivalent circuit model 10, an internal impedance of the battery 3 isrepresented by the following equation (1) when Laplace transform isperformed.

$\begin{matrix}{{{ZO}(s)} = {{RO} + \frac{R\; 1}{1 + {{sC}\; 1R\; 1}} + \frac{R\; 2}{1 + {{sC}\; 2R\; 2}} + \frac{Dw}{\sqrt{s}}}} & (1)\end{matrix}$

First to third terms on the left side of the equation 1 correspond to animpedance of a circuit including the resistor 12, the resistor 13, thecapacitor 14, the resistor 15, and the capacitor 16. For example, thesecond term corresponds to an impedance of the CR circuit including theresistor 13 and the capacitor 14. The third term corresponds to animpedance of the CR circuit including the resistor 15 and the capacitor16.

A fourth term on the left side of the equation 1 corresponds to Zw whichis an impedance of the Warburg impedance 17. s is a value obtained byperforming Laplace transform on jω with respect to an angular frequencyω. Dw is a Warburg coefficient.

In order to analyze a predetermined current-voltage waveform instead ofan ideal step current waveform, it is appropriate to use analysis byZ-transform. Meanwhile, it is difficult to perform Z-transform on thefourth term on the left side corresponding to the Warburg impedance 17in the equation (1). Therefore, the following approximate equation isintroduced.

FIG. 3 is a diagram illustrating an equivalent circuit of a Warburgimpedance. An equivalent circuit 170 is an equivalent circuit model ofthe Warburg impedance 17 using a fifth-order foster type series circuit,

The equivalent circuit 170 includes a CR circuit in which a resistor 21and a capacitor 31 are coupled in parallel, a CR circuit in which aresistor 22 and a capacitor 32 are coupled in parallel, and a CR circuitin which a resistor 23 and a capacitor 33 are coupled in parallel. Theequivalent circuit 170 includes a CR circuit in which a resistor 24 anda capacitor 34 are coupled in parallel, and a CR circuit in which aresistor 25 and a capacitor 35 are coupled in parallel. In theequivalent circuit 170, the respective CR circuits described above arecoupled in series. A time constant of each CR circuit is steps of apower of 10.

A resistance value of the resistor 21 is Rw1. A resistance value of theresistor 22 is Rw2. A resistance value of the resistor 23 is Rw3. Aresistance value of the resistor 24 is Rw4, A resistance value of theresistor 25 is Rw5.

A capacitance of the capacitor 31 is Cw1. A capacitance of the capacitor32 is Cw2.A capacitance of the capacitor 33 is Cw3. A capacitance of thecapacitor 34 is Cw4. A capacitance of the capacitor 35 is Cw5.

In a case where the Warburg impedance 17 is represented by theequivalent circuit 170, Zw which is an impedance may be approximated asrepresented by the following equation (2).

$\begin{matrix}{{{Zw}(s)} = {\frac{Dw}{\sqrt{s}} \approx {{Dw}{\sum_{i = 1}^{5}\frac{Rwi}{1 + {sCwiRwi}}}}}} & (2)\end{matrix}$

Rw1 to Rw5 and Cw1 to Cw5 obtained by minimizing an error functionrepresented by the following equation (3) are values of respectiveparameters in a case where the Warburg impedance 17 is represented bythe equivalent circuit 170. E represents an error function. In thiscalculation, s is jω which is a value of z in a case of using an idealstep function to verify a frequency response.

$\begin{matrix}{E = {\left\{ {{Re}\left\lbrack {\frac{1}{\sqrt{s}} - {\sum_{i = 1}^{5}\frac{Rwi}{1 + {sCwiRwi}}}} \right\rbrack} \right\}^{2} + \left\{ {{Im}\left\lbrack {\frac{1}{\sqrt{s}} - {\sum_{i = 1}^{5}\frac{Rwi}{1 + {sCwiRwi}}}} \right\rbrack} \right\}^{2}}} & (3)\end{matrix}$

FIG. 4 is a diagram illustrating an example of a parameter value in acase where a Warburg impedance is represented by an equivalent circuit.The number of the uppermost stage in FIG. 4 indicates a number of stagesof the CR circuit in the equivalent circuit 170, and corresponds to anumber obtained in a case where the number is counted from left to rightin the CR circuit. Rw1, which is a resistance value of the resistor 21in the CR circuit in the first stage, is 0.144 Ω, and Cw1, which is acapacitance of the capacitor 31, is 0.110 F. Rw2,which is a resistancevalue of the resistor 22 in the CR circuit in the second stage, is 0.270Ω, and Cw2, which is a capacitance of the capacitor 32, is 0.590 F. Rw3,which is a resistance value of the resistor 23 in the CR circuit in thethird stage, is 0.953 Ω, and Cw3, which is a capacitance of thecapacitor 33, is 1.67 F. Rw4, which is a resistance value of theresistor 24 in the CR circuit in the fourth stage, is 2.90 Ω, and Cw4,which is a capacitance of the capacitor 34, is 5.49 F. Rw5, which is aresistance value of the resistor 25 in the CR circuit in the fifthstage, is 12.9 Ω, and Cw5, which is a capacitance of the capacitor 35,is 12.3 F.

Accuracy of Rw1 to Rw5 and Cw1 to Cw5 representing the obtained Warburgimpedance 17 will be verified. An approximate solution of the errorfunction is obtained by overlapping first-order low pass filter (LPF)characteristics. FIG. 5 is a diagram for explaining an overlap of thefirst-order LPF characteristics. A graph 201 in FIG. 5 is a graphrepresenting a real number component. A graph 202 is a graphrepresenting an imaginary component.

Lines 211 to 215 in the graph 201 represent real number components ofLPF characteristics in a case using of Rw1 to Rw5 and Cw1 to Cw5obtained by using the equation (3). The line 211 represents a LPFcharacteristic of the CR circuit including the resistor 21 and thecapacitor 31 having a resonant frequency of 10 Hz. The line 212represents a LPF characteristic of the CR circuit including the resistor22 and the capacitor 32 having a resonant frequency of 1 Hz. The line213 represents a LPF characteristic of the CR circuit including theresistor 23 and the capacitor 33 having a resonance frequency of 100MHz. The line 214 represents a LPF characteristic of the CR circuitincluding the resistor 24 and the capacitor 34 having a resonantfrequency of 10 MHz. The line 215 represents a LPF characteristic of theCR circuit including the resistor 25 and the capacitor 5 having aresonant frequency of 1 MHz. When the lines 211 to 215 are overlappedwith one another, a line 216 is obtained. This line 216 becomes anapproximate solution of real number components in a case where theWarburg impedance 17 is represented by the equivalent circuit 170.

Lines 221 to 225 in the graph 202 represent imaginary components of LPFcharacteristics in a case of using Rw1 to Rw5 and Cw1 to Cw5 obtained byusing the equation (3). The line 221 represents a LPF characteristic ofthe CR circuit including the resistor 21 and the capacitor having aresonant frequency of 10 Hz. The line 222 represents a LPFcharacteristic of the CR circuit including the resistor 22 and thecapacitor 2 having a resonant frequency of 1 Hz. The line 223 representsa LPF characteristic of the CR circuit including the resistor 23 and thecapacitor 33 having a resonance frequency of 100 MHz. The line 224represents a LPF characteristic of a CR circuit including the resistor24 and the capacitor 34 having a resonant frequency of 10 MHz. The line225 represents a LPF characteristic of a CR circuit including theresistor 25 and the capacitor 35 having a resonant frequency of 1 MHz.When the lines 221 to 225 are overlapped with one another, a line 226 isobtained. This line 226 becomes an approximate solution of imaginarycomponents in a case where the Warburg impedance 17 is represented bythe equivalent circuit 170.

The approximate solution of the imaginary component and the real numbercomponent in the case where the Warburg impedance 17 is represented bythe equivalent circuit 170 is compared with an actual measurement valueof a response characteristic of the Warburg impedance 17. FIG. 6 is adiagram illustrating a comparison between an estimated waveform using anapproximate solution and a waveform based on an actual measurementvalue.

A graph 203 in FIG. 6 is a graph illustrating a comparison between anestimated waveform of a frequency response characteristic and a waveformof an actual measurement. A line 231 represents a real number componentof an estimated waveform using an approximate solution calculated basedon the equivalent circuit 170. A line 232 represents an imaginarycomponent of the estimated waveform using the approximate solutioncalculated based on the equivalent circuit 170. A line 233 represents areal number component of a waveform obtained from an actual measurementvalue of a frequency response characteristic of the Warburg impedance17. A line 234 represents an imaginary component of another waveformobtained from the actual measurement value of the frequency responsecharacteristic of the Warburg impedance 17.

In the graph 203, 500 Hz to 0.5 Hz is a frequency range of 3 digits. Asillustrated in the graph 203, the approximate solution of the realnumber component in the case where the Warburg impedance 17 isrepresented by the equivalent circuit 170 is approximated to the actualmeasurement value of the frequency response characteristic of theWarburg impedance 17 in the frequency range of 500 Hz to 0.5 Hz. Forexample, the equivalent circuit 170 may accurately represent the Warburgimpedance 17 in the frequency range of 3 digits.

A graph 204 is a graph illustrating a comparison between an estimatedwaveform of a transient response characteristic and a waveform of a realmeasurement. A line 241 represents an approximate solution of atransient response characteristic in a case of using the equivalentcircuit 170. A line 242 represents an actual measurement value. In thismanner, for the transient response characteristic, it may also be saidthat the approximate solution is approximate to the actual measurementvalue. Also in this point, the equivalent circuit 170 accuratelyrepresents the Warburg impedance 17.

FIG. 7 is a block diagram of a deterioration diagnosis server. Asillustrated in FIG. 7, the deterioration diagnosis server 1 includes adeterioration state analysis unit 100, a deterioration diagnosis unit101, and a notification unit 102. The deterioration state analysis unit100 includes a data obtainment unit 111, an initial value setting unit112, a storage unit 113, a random number generation unit 114, anestimated voltage waveform calculation unit 115, and an error comparisonunit 116. The deterioration diagnosis server 1 is an example of a“battery deterioration diagnosis apparatus”, and the deterioration stateanalysis unit 100 is an example of a “battery deterioration analysiscircuit”.

The storage unit 113 holds values of Rw1 to Rw5 and Cw1 to Cw5 in thecase where the Warburg impedance 17 is represented by using theequivalent circuit 170.

The data obtainment unit 111 receives inputs of a voltage value and acurrent value of each battery 3 from the data collection system 2. Thedata obtainment unit 111 outputs the obtained voltage value and currentvalue of each battery 3 to the estimated voltage waveform calculationunit 115. The data obtainment unit 111 notifies the initial valuesetting unit 112 of a start of a deterioration state determinationprocess. The data obtainment unit 111 corresponds to an example of an“obtainment unit”.

The initial value setting unit 112 receives the notification of thestart of the deterioration state determination process from the dataobtainment unit 111. The initial value setting unit 112 sets R0 to R3,which are resistance values of the resistors 12, 13, and 15, and setsinitial values of C1 and C2, which are capacitances of the capacitors 14and 16, in a case where the battery 3 is represented by the equivalentcircuit model 10. The initial value setting unit 112 sets an initialvalue of Dw, which is a Warburg coefficient of the Warburg impedance 17.

The deterioration state analysis unit 100 estimates an equivalentcircuit parameter of the equivalent circuit model 10 for the battery 3,and performs optimization by repeating the estimation process using aMonte Carlo method. In the first estimation process, the initial valuesetting unit 112 sets an appropriate value to an initial value of theequivalent circuit parameter. On the other hand, after the secondestimation process, the initial value setting unit 112 obtains values ofequivalent circuit parameters stored in the storage unit 113, and setsthe values to initial values of R0 to R3, C1 and C2, and Dw.

Thereafter, the initial value setting unit 112 outputs the initial valueof the equivalent circuit parameter to the random number generation unit114. When an execution request of the estimation process is receivedfrom the error comparison unit 116, the initial value setting unit 112executes the setting and the output of the initial value of theequivalent circuit parameter again.

The random number generation unit 114 receives the input of the initialvalue of the equivalent circuit parameter from the initial value settingunit 112. The random number generation unit 114 generates a randomnumber for each equivalent circuit parameter by using the obtainedinitial value.

The random number generation unit 114 gradually reduces generationdeviation of a random number every time the estimation process isrepeated, and converges a value of the equivalent circuit parameter. Forexample, in the first estimation process, the random number generationunit 114 generates a random number with a random number generationdeviation of 10%. Thereafter, the random number generation unit 114reduces the random number generation deviation to 5%, 1%, and 0.5% foreach repetition of the estimation process. The random number generationunit 114 outputs the generated random number for each equivalent circuitparameter to the estimated voltage waveform calculation unit 115 as avalue of each equivalent circuit parameter.

Thereafter, when receiving a re-execution request for the random numbergeneration process from the error comparison unit 116, the random numbergeneration unit 114 executes again the random number generation for eachequivalent circuit parameter by using the initial value. The randomnumber generation unit 114 repeats the process of outputting thegenerated random number to the estimated voltage waveform calculationunit 115 as a value of each equivalent circuit parameter.

The estimated voltage waveform calculation unit 115 receives an input ofmeasurement data of a voltage and measurement data of a current from thedata obtainment unit 111. The estimated voltage waveform calculationunit 115 receives the input of the value of each equivalent circuitparameter from the random number generation unit 114. Next, theestimated voltage waveform calculation unit 115 obtains a value obtainedby performing Z-transform on the voltage measurement data. The estimatedvoltage waveform calculation unit 115 calculates an error value betweenthe Z-transformed actual measurement value and the estimated value. Thecalculation of the error value will be described in detail below,

The estimated voltage is represented by the following equation (4).Ve(t) represents estimated voltage data. OCV is an open circuit voltage.Z0 represents an internal impedance. Im(t) represents currentmeasurement data.

Ve(t)=OCV−ZOIm(t)   (4)

Next, Laplace transform is performed on the equation (4), and thefollowing equation (5) is obtained. Ve(s) is estimated voltage data onwhich Laplace transform is performed. Z0(s) is an internal impedance onwhich Laplace transform is performed. Im(s) is current measurement dataon which Laplace transform is performed.

Ve(s)=OCV−ZO(s)Im(s)   (5)

Next, Z-transform is performed on the equation (5), and the followingequation (6) is obtained. Ve(z) is estimated voltage data on whichZ-transform is performed. Z0(z) is an internal impedance on whichZ-transform is performed. Im(z) is current measurement data on whichZ-transform is performed.

Ve(z)=OCV−ZO(z)Im(z)   (6)

Ez, which is an average square error between the estimated voltage datarepresented by the equation (6) and actual measurement voltage data, isrepresented by the equation (7). Vm(zi) is voltage measurement data ofthe i-th sample on which Z-transform is performed. Ve(zi) is estimatedvoltage data corresponding to the voltage measurement data of the i-thsample on which Z-transform is performed. Z0(zi) is an internalimpedance corresponding to the voltage measurement data of the i-thsample on which Z-transform is performed. Im(zi) is current measurementdata of the i-th sample on which Z-transform is performed N is thenumber of samples.

$\begin{matrix}{{Ez} = {\sqrt{\frac{1}{N}{\sum_{i = 1}^{N}\left\{ {{{Ve}({zi})} - {{Vm}({zi})}} \right\}^{2}}} = \sqrt{\frac{1}{N}{\sum_{i = 1}^{N}\left\{ {{OCV} - {{{ZO}({zi})}{{Im}({zi})}} - {{Vm}({zi})}} \right\}^{2}}}}} & (7)\end{matrix}$

The estimated voltage waveform calculation unit 115 obtains Z0(zi) whichis a Z-transformed internal impedance which minimizes Ez, which is amean square error represented in the equation (7). Z0(z) which is aZ-transformed internal impedance is represented by the followingequation (8).

$\begin{matrix}{{Z\; 0(z)} = {{R\; 0} + {\sum_{i = 1}^{2}\frac{{RiT} + {RiTz}^{- 1}}{T + {2C_{i}R_{i}} + {\left( {T - {2C_{i}R_{i}}} \right)Z} - 1}} + {{Dw}{\sum_{i = 1}^{5}\frac{{RwiT} + {RwiTz}^{- 1}}{T + {2{CwiRwi}} + {\left( {T - {2{CwiRwi}}} \right)Z^{- 1}}}}}}} & (8)\end{matrix}$

The estimated voltage waveform calculation unit 115 calculates R0 to R2,C1, C2, and Dw, which are equivalent circuit parameters which minimizeEz, which is a mean square error illustrated in the equation (7), byusing the equations (7) and (8). The estimated voltage waveformcalculation unit 115 outputs the calculated minimum mean square errorand the equivalent circuit parameter to the error comparison unit 116.

The error comparison unit 116 receives the input of the mean squareerror and the equivalent circuit parameter from the estimated voltagewaveform calculation unit 115. In a case of the first estimationprocess, the mean square error is not yet stored in the storage unit113. In the first estimation process, the error comparison unit 116stores the mean square error obtained from the error comparison unit 116in the storage unit 113. Thereafter, the error comparison unit 116outputs an execution request for the estimation process to the initialvalue setting unit 112.

On the other hand, in a case of the second and subsequent estimationprocesses, the error comparison unit 116 compares a mean square errorstored in the storage unit 113 with a mean square error obtained fromthe estimated voltage waveform calculation unit 115. In a case where themean square error obtained from the estimated voltage waveformcalculation unit 115 is smaller than the mean square error stored in thestorage unit 113, the error comparison unit 116 updates the mean squareerror stored in the storage unit 113 into the mean square error obtainedfrom the estimated voltage waveform calculation unit 115. The errorcomparison unit 116 updates an equivalent circuit parameter stored inthe storage unit 113 by changing the equivalent circuit parameter to anequivalent circuit parameter obtained from the estimated voltagewaveform calculation unit 115. Thereafter, the error comparison unit 116outputs an execution request for the estimation process to the initialvalue setting unit 112.

On the other hand, in a case where the mean square error obtained fromthe estimated voltage waveform calculation unit 115 is equal to orgreater than the mean square error stored in the storage unit 113, theerror comparison unit 116 determines whether or not the number ofrepetitions of the equivalent circuit parameter convergence process fromrandom number generation to error comparison is equal to or more than aconvergence process count. In a case where the number of repetitions isless than the convergence process count, the error comparison unit 116outputs an execution request of the random number generation process tothe random number generation unit 114.

On the other hand, in a case where the number of repetitions is equal toor more than the convergence process count, the error comparison unit116 determines whether or not the number of times an initial value isset is equal to or greater than an estimation process count. In a casewhere the number of initial value settings is less than the estimationprocess count, the error comparison unit 116 outputs an executionrequest for the estimation process to the initial value setting unit112. On the other hand, in a case where the number of initial valuesettings is equal to or more than the estimation process count, theerror comparison unit 116 determines the equivalent circuit parameter tobe a value stored in the storage unit 113. Thereafter, the errorcomparison unit 116 outputs a completion notification of the analysis ofthe deterioration state to the deterioration diagnosis unit 101.

The estimated voltage waveform calculation unit 115 and the errorcomparison unit 116 correspond to examples of an “analysis unit”.

The deterioration diagnosis unit 101 receives the input of thecompletion notification of the analysis of the deterioration state fromthe error comparison unit 116. The deterioration diagnosis unit 101obtains the equivalent circuit parameter from the storage unit 113.Thereafter, the deterioration diagnosis unit 101 obtains an index valueby using the equivalent circuit parameter, and determines adeterioration state of the battery 3 by using the obtained index value.

For example, the deterioration diagnosis unit 101 obtains R0+R1+R2 as anindex value. In a case where R0+R1+R2 exceeds a predetermineddeterioration threshold value, the deterioration diagnosis unit 101determines that the battery 3 is deteriorated. The deteriorationthreshold value is, for example, 2 times an index value of the battery 3in an unused state.

Usually, in the equivalent circuit model 10, among the equivalentcircuit parameters, R0 represents an electric field flow, and R1 and R2represent electrodes. The deterioration diagnosis unit 101 may specify adeteriorated portion based on a type of the equivalent parameterdetermined to be deteriorated among R0 to R2.

When detecting the deterioration of the battery 3, the deteriorationdiagnosis unit 101 notifies the notification unit 102 of occurrence ofthe deterioration of the battery 3.

The notification unit 102 receives the notification of the occurrence ofthe deterioration of the battery 3 from the deterioration diagnosis unit101. The notification unit 102 notifies the manager of the occurrence ofthe deterioration of the battery 3. For example, the notification unit102 causes the display unit to display a message for notifying theoccurrence of the deterioration of the battery 3, so the occurrence ofthe deterioration of the battery 3 is notified to the manager.

Next, a flow of the estimation process of the equivalent circuitparameter will be described with reference to FIG. 8. FIG. 8 is aflowchart of an estimation process of an equivalent circuit parameter.

The data obtainment unit 111 outputs voltage measurement data andcurrent measurement data obtained from the data collection system 2 tothe estimated voltage waveform calculation unit 115, and also instructsthe initial value setting unit 112 to start an estimation process ofequivalent circuit parameters. When the instruction for estimating theequivalent circuit parameter is received, the initial value setting unit112 sets an initial value of each equivalent circuit parameter (stepS1). The initial value setting unit 112 outputs the initial value of theequivalent circuit parameter to the random number generation unit 114.

The random number generation unit 114 receives the input of the initialvalue of each equivalent circuit parameter from the initial valuesetting unit 112. The random number generation unit 114 generates arandom number by using the initial value for each equivalent circuitparameter (step S2). The random number generation unit 114 outputs thegenerated random number for each equivalent circuit parameter to theestimated voltage waveform calculation unit 115.

The estimated voltage waveform calculation unit 115 receives the inputof the random number for each equivalent circuit parameter from therandom number generation unit 114. The estimated voltage waveformcalculation unit 115 obtains the voltage measurement data and thecurrent measurement data from the data obtainment unit 111 (step S3).

Next, the estimated voltage waveform calculation unit 115 calculates amean square error by using the equation (7) (step S4). The estimatedvoltage waveform calculation unit 115 obtains a value of the equivalentcircuit parameter which minimizes a mean square error between an actualmeasurement voltage value and an estimated voltage value by using theequation (8). Thereafter, the estimated voltage waveform calculationunit 115 outputs the minimum value of the mean square error and theobtained value of the equivalent circuit parameter to the errorcomparison unit 116.

The error comparison unit 116 receives the input of the minimum value ofthe mean square error between the actual measurement voltage value andthe estimated voltage value from the estimated voltage waveformcalculation unit 115. Next, the error comparison unit 116 determineswhether or not the calculated value of the mean square error by theestimated voltage waveform calculation unit 115 is less than a storedvalue of a mean square error stored in the storage unit 113 (step S5).In a case where the calculated value is equal to or greater than thestored value (NO in step S5), the error comparison unit 116 proceeds tostep S7.

On the other hand, in a case where the calculated value is less than thestored value (YES in step S5), the error comparison unit 116 storesvalues of the equivalent circuit parameter and the mean square error inthe storage unit 113, and updates the values thereof (step S6).

Next, the error comparison unit 116 determines whether or not the numberof repetitions of a convergence process of the equivalent circuitparameter reaches a convergence process count (step S7). In a case wherethe number of repetitions does not reach the convergence process count(NO in step S7), the error comparison unit 116 requests the randomnumber generation unit 114 to generate a random number, and the processreturns to step S2.

On the other hand, in a case where the number of repetitions reaches theconvergence process count (YES in step S7), the error comparison unit116 determines whether or not the number of initial value settingsreaches an estimation process count (step S8). In a case where thenumber of repetitions does not reach the estimation process count (NO instep S8), the error comparison unit 116 requests the initial valuesetting unit 112 to set the initial value, and the process returns tostep S1.

On the other hand, in a case where the number of repetitions reaches theestimation process count (YES in step S8), the estimation process of theequivalent circuit parameter is completed, and a value stored in thestorage unit 113 at that time is determined as a value of the equivalentcircuit parameter of the equivalent circuit model 10 representing thebattery 3.

Next, an overall flow of a deterioration diagnosis process performed bythe deterioration diagnosis server 1 will be described with reference toFIG. 9. FIG. 9 is a flowchart of the deterioration diagnosis process.

The deterioration state analysis unit 100 obtains voltage measurementdata and current measurement data of the battery 3 from the datacollection system 2 (step S21).

Next, the deterioration state analysis unit 100 executes a calculationprocess of an equivalent circuit parameter (step S22). The processillustrated in the flowchart in FIG. 8 is an example of the calculationprocess of the equivalent circuit parameter to be executed in step S22.Thereafter, the deterioration state analysis unit 100 notifies thedeterioration diagnosis unit 101 of completion of analysis of adeterioration state.

The deterioration diagnosis unit 101 obtains the equivalent circuitparameter from the storage unit 113. Thereafter, the deteriorationdiagnosis unit 101 obtains an index value by using the equivalentcircuit parameter (step S23).

The deterioration diagnosis unit 101 determines whether or not the indexvalue is equal to or greater than a deterioration threshold value (stepS24). A case where the deterioration threshold value represents an upperlimit of the index value will be described. In a case where the indexvalue is less than the deterioration threshold value (NO in step S24),the deterioration diagnosis unit 101 determines that the battery 3 isnot deteriorated, and the deterioration diagnosis server 1 returns tostep S21.

On the other hand, in a case where the index value is equal to orgreater than the deterioration threshold value (YES in step S24), thedeterioration diagnosis unit 101 notifies the notification unit 102 ofdetection of deterioration occurrence of the battery 3. In response tothe notification from the deterioration diagnosis unit 101, thenotification unit 102 notifies the manager of the occurrence ofdeterioration in the battery 3 (step S25).

Next, an example of an analysis result of an internal impedance will bedescribed with reference to FIG. 10. FIG. 10 is a diagram illustratingthe example of the analysis result of the internal impedance. A line 256in FIG. 10 is an actual measurement value of an open voltage of acertain battery 3. On the other hand, the deterioration diagnosis server1 calculates equivalent circuit parameters of the battery 3 as R0=4.6mΩ, R1=5.4 mΩ, R2=2.7 mΩ, C1=3.9 F, C2=19 F, and Dw=8.3 m. In this case,a mean square error of the voltage measurement data and the estimatedvoltage data is 0.125 mV.

In FIG. 10, a line 251 represents a voltage drop caused by the resistor12 in the equivalent circuit model 10. A line 252 represents a voltagedrop caused by the CR circuit including the resistor 13 and thecapacitor 14. A line 253 represents a voltage drop caused by the CRcircuit including the resistor 15 and the capacitor 16. The line 253also represents a voltage drop caused by the Warburg impedance 17. Thelines 251 to 253 are obtained by using the equivalent circuit parametercalculated by the deterioration diagnosis server 1.

A sum of respective components of the lines 251 to 254 is a line 255.The line 255 is approximate to the line 256 which is actual measurementdata, and it may be seen that the deterioration state analysis unit 100accurately generates a transient response waveform.

Next, accuracy of the deterioration diagnosis will be described withreference to FIGS. 11 to 14. FIG. 11 is a diagram illustrating anestimated value of an equivalent circuit parameter in a case where abattery of 4.5 Ah is used. FIG. 12 is a diagram illustrating an actualmeasurement value in a case where a battery of 4.5 Ab is used, FIG. 13is a diagram illustrating an estimated value of an equivalent circuitparameter in a case where a battery of 8.0 Ah is used. FIG. 14 is adiagram illustrating an actual measurement value in a case where abattery of 8.0 Ah is used.

As illustrated in FIG, 11, in an initial state before use of a certainbattery 3 of 4.5 Ah, the deterioration diagnosis server 1 calculatesequivalent circuit parameters as R0=4.1 mΩ, R1=19 mΩ, R2=6.1 mΩ, C1=2.0F, C2=22 F, and Dw=15 m. After 32 cycles for the same battery 3 having4.5 Ah, the deterioration diagnosis server 1 calculates equivalentcircuit parameters as R0=5.6 mΩ, R1=18 mΩ, R2=21 mΩ, C1=1.7 F, C2=5.6 F,and Dw=14 m. In this case, since R2 changes greatly from 6.1 mΩ to 21mΩ, deterioration diagnosis server 1 may detect occurrence ofdeterioration in the battery 3.

On the other hand, with reference to FIG. 12, a transient waveformillustrated by a line 261, for example, is obtained from actualmeasurement data in an initial state before use of the same battery 3having 4.5 Ah. A transient response waveform indicated by a line 262 isobtained from actual measurement data after 32 cycles of the samebattery 3 having 4.5 Ah. In this manner, it may be confirmed that thebattery 3 is also deteriorated over the actual measurement data, and thedeterioration diagnosis by the deterioration diagnosis server 1 isaccurate.

As illustrated in FIG. 13, in an initial state before use of a certainbattery 3 of 8.0 Ah, the deterioration diagnosis server 1 calculatesequivalent circuit parameters as R0=3.3 mΩ, R1=12 mΩ, R2=5.9 mΩ, C1=4.3F, C2=30 F, and Dw=9.7 m. After 32 cycles for the same battery 3 having8.0 Ah, the deterioration diagnosis server 1 calculates equivalentcircuit parameters as R0=5.4 mΩ, R1=18 mΩ, R2=18 mΩ, C1=3.4 F, C2=12 F,and Dw=7.4 m. In this case, since R2 changes greatly from 5.9 mΩ to 18mΩ, the deterioration diagnosis server 1 may detect occurrence ofdeterioration in the battery 3.

On the other hand, with reference to FIG. 14, a transient responsewaveform illustrated by a line 271, for example, is obtained from actualmeasurement data in the initial state before use of the same battery 3having 8.0 Ah. A transient response waveform indicated by a line 272 isobtained from actual measurement data after 32 cycles of the samebattery 3 having 8.0 Ah. In this manner, it may be confirmed that thebattery 3 is also deteriorated over the actual measurement data, and thedeterioration diagnosis by the deterioration diagnosis server 1 isaccurate.

(Hardware Configuration)

Next, a hardware configuration of the deterioration diagnosis server 1will be described with reference to FIG. 15, FIG. 15 is a hardwareconfiguration diagram of a deterioration diagnosis server.

The deterioration diagnosis server 1 includes a central processing unit(CPU) 91, a memory 92, a storage 93, and an external interface 94. Adisplay 95 is coupled to the deterioration diagnosis server 1.

The external interface 94 is coupled to the data collection system 2.The external interface 94 transmits data obtained from the datacollection system 2 to the CPU 91 via a bus.

The CPU 91 is coupled to the memory 92, the storage 93, the externalinterface 94, and the display 95 via the bus. The CPU 91 transmits andreceives data to and from the memory 92, the storage 93, the externalinterface 94, and the display 95 via the bus.

The storage 93 is a storage device such as a hard disk, a solid statedrive (SSD), or the likes The storage 93 realizes a function of thestorage unit 113 illustrated in FIG. 7, for example. The storage 93stores various programs including programs for realizing functions ofthe data obtainment unit 111, the initial value setting unit 112, therandom number generation unit 114, the estimated voltage waveformcalculation unit 115, the error comparison unit 116, the deteriorationdiagnosis unit 101, and the notification unit 102 illustrated in FIG. 7.

The CPU 91 reads various programs from the storage 93, expands theprograms onto the memory 92, and executes the programs. Accordingly, theCPU 91 and the memory 92 realize functions of the data obtainment unit111, the initial value setting unit 112, the random number generationunit 114, the estimated voltage waveform calculation unit 115, the errorcomparison unit 116, the deterioration diagnosis unit 101, and thenotification unit 102 illustrated in FIG. 7.

In this embodiment, the case where the deterioration diagnosis server 1includes the deterioration state analysis unit 100, the deteriorationdiagnosis unit 101, and the notification unit 102 is described, but theembodiment may have another configuration. For example, a device havinga function of the deterioration state analysis unit 100 may be disposed,and a device having the functions of the deterioration diagnosis unit101 and the notification unit 102 may perform deterioration diagnosisbased on an equivalent circuit parameter output from the device.

As described above, the deterioration diagnosis server according to thepresent embodiment estimates a transient response waveform based on anequivalent circuit model of a battery represented by using anapproximate solution of a Warburg impedance obtained by using anequivalent circuit including CR circuits of 5 stages. The deteriorationdiagnosis server performs deterioration diagnosis on the battery byusing equivalent circuit parameters corresponding to the estimatedtransient response waveform.

By calculating an approximate solution of a Warburg impedance using theequivalent circuit including the CR circuits of 5 stages, it is possibleto analyze a frequency of 3 digits with a filter having a resonancefrequency of 5 digits. In a case where a time constant of the CR circuitof several 10 of msec is analyzed, a range of a sampling frequency is 1kHz. According to a sampling theorem, the frequency of 1 kHz does notinclude information equal to or more than 500 Hz. For analysis for onesecond, it is desirable to perform the analysis up to a frequency of 0.5Hz in a frequency range. For example, in a case where a time constant ofthe CR circuit of several 10 of msec is analyzed, it is preferable toanalyze a frequency of 3 digits.

In this respect, in a case where a normal foster type equivalent circuitis used, a step of a time constant of CR circuits is performed at(2n−1)². For example, in order to analyze the frequency of 3 digits byusing the normal foster type equivalent circuit, 16 CR circuits areused. On the other hand, in the equivalent circuit according to thepresent embodiment, a step of a time constant of CR circuits isperformed at 10^(n). For example, in order to analyze the frequency of 3digits by using the equivalent circuit according to the presentembodiment, at least three CR circuits may be used. In the diagnosisserver according to the present embodiment, the equivalent circuit usingthe 5 CR circuits is used to accurately analyze the frequency of 3digits.

As described above, in the equivalent circuit model used by thedeterioration diagnosis server according to the present embodiment, itis possible to analyze the frequency of 3 digits by approximating theWarburg impedance with the equivalent circuit including the CR circuitsof 5 stages, and it is possible to calculate the Warburg impedance witha small amount of calculation. For example, in the equivalent circuitmodel used by the deterioration diagnosis server according to thepresent embodiment, the Warburg impedance is obtained in a calculationtime of one-third of that in a case where a normal foster typeequivalent circuit is used.

The deterioration diagnosis server according to the present embodimentperforms deterioration diagnosis on the battery by using an equivalentcircuit model using a Warburg impedance with high accuracy, so itpossible to perform deterioration diagnosis with high accuracy. Forexample, the deterioration diagnosis server according to the presentembodiment may accurately perform life diagnosis on a storage batterywith a small amount of calculation.

All examples and conditional language provided herein are intended forthe pedagogical purposes of aiding the reader in understanding theinvention and the concepts contributed by the inventor to further theart, and are not to be construed as limitations to such specificallyrecited examples and conditions, nor does the organization of suchexamples in the specification relate to a showing of the superiority andinferiority of the invention. Although one or more embodiments of thepresent invention have been described in detail, it should be understoodthat the various changes, substitutions, and alterations could be madehereto without departing from the spirit and scope of the invention.

What is claimed is:
 1. An information processing apparatus comprising: amemory; and a processor coupled to the memory and configured to: obtainan actual measurement voltage at a time of a voltage change of abattery; estimate an internal impedance of the battery based on anequivalent circuit model of the battery in which a Warburg impedance isrepresented by an approximate equation using an equivalent circuit whichis a series circuit of CR circuits and has steps of a power of 10 as atime constant of the CR circuit and the actual measurement voltage;determine a deterioration state of the battery based on the internalimpedance; and notify of deterioration of the battery in a case wherethe deterioration diagnosis unit detects deterioration.
 2. Theinformation processing apparatus according to claim 1 wherein theequivalent circuit includes the five CR circuits.
 3. The informationprocessing apparatus according to claim 1 wherein the approximateequation is an equation which approximates a calculation result obtainedby Z-transform on a Warburg impedance.
 4. The information processingapparatus according to claim 1, wherein the processor is configured to:obtain an actual measurement current; calculate an equivalent circuitparameter included in the equivalent circuit model in which an errorbetween an estimated voltage calculated based on the equivalent circuitmodel and the actual measurement current and the actual measurementvoltage is minimized; and determine a deterioration state of the batterybased on the equivalent circuit parameter.
 5. An information processingapparatus comprising: a memory; and a processor coupled to the memoryand configured to: obtain an actual measurement voltage at a time of avoltage change of a battery; and estimate an internal impedance of thebattery based on an equivalent circuit model of the battery in which aWarburg impedance is represented by an approximate equation using anequivalent circuit which is a series circuit of CR circuits and hassteps of a power of 10 as a time constant of the CR circuit and theactual measurement voltage.
 6. A non-transitory computer-readablerecording medium storing a battery deterioration diagnosis programcausing a computer to execute a process, the process comprising:obtaining an actual measurement voltage at a time of a voltage change ofa battery; estimating an internal impedance of the battery based on anequivalent circuit model of the battery in which a Warburg impedance isrepresented by an approximate equation using an equivalent circuit whichis a series circuit of CR circuits and has steps of a power of 10 as atime constant of the CR circuit and the obtained actual measurementvoltage; determining a deterioration state of the battery based on theestimated internal impedance; and notifying of deterioration of thebattery in a case where the deterioration is detected.
 7. Thenon-transitory computer-readable recording medium according to claim 6,wherein the equivalent circuit includes the five CR circuits.
 8. Thenon-transitory computer-readable recording medium according to claim 6,wherein the approximate equation is an equation which approximates acalculation result obtained by Z-transform on a Warburg impedance. 9.The non-transitory computer-readable recording medium according to claim6, further comprising: obtaining an actual measurement current,calculating an equivalent circuit parameter included in the equivalentcircuit model in which an error between an estimated voltage calculatedbased on the equivalent circuit model and the actual measurement currentand the actual measurement voltage is minimized; and determining adeterioration state of the battery based on the equivalent circuitparameter.